The Britons were in second place after the Super-G section but could not edge ahead of Slovakia’s Henrieta Farkasova and her guide Natalia Subrtova.
Compatriots Millie Knight and Brett Wild just missed out on a medal in fourth, while Kelly Gallagher and Gary Smith ended up seventh.
GB can thrive with 'target on their backs' at Paralympics, says Love
"Today we went for it and it was really awesome," Fitzpatrick, who was born with congenital retinal folds and has only limited sight in her right eye, with none in her left, told the BBC.
"I wasn't impressed with my skiing on Sunday because I was quite static and wasn't getting in the tuck when Jen was shouting at me to.
"But after the individual Super G we knew we had one medal in the bag. Now we are just having a fabulous time and enjoying the Paralympics because often you go through the race and just think about skiing."
The British pair ended up with an overall time of 2 mins 29 secs, just 1.78secs behind the Slovakian pair. Melissa Perrine and Christian Geiger of Australia took bronze.
Christiansen: Back in the saddle and in the hunt for more Paralympic success
Becoming an athlete was never my dream, says Paralympic medallist Cockroft